Methods, systems, apparatus, and circuits for dynamically optimizing the circuit for forward and backward propagation phases of training for neural networks, given a fixed resource budget. The circuits comprising: (1) a specialized circuit that can operate on a plurality of multi-dimensional inputs and weights for the forward propagations phase of neural networks; and (2) a specialized circuit that can operate on either gradients and inputs, or gradients and weights for the backward propagation phase of neural networks. The method comprising: (1) an analysis step to obtain the number of operations and the precision of operations in the forward and backward propagations phases of the neural network; (2) a sampling step to obtain the number of zero-valued activations and gradients during the execution of the neural network; (3) a scheduling and estimation step to obtain the runtime for the forward and backward phases of neural network execution using specialized circuits; (4) a builder step to apply the optimal breakdown of resource budget for the forward and backward phases of the neural network to improve the execution of the Neural Network training for future iterations.